Nope. New landlords are incentivized to build housing. The only thing that could stop them is regulations from existing landlords, but in a place with enough votes for rent control or subsidies, existing landlords do not have the votes to stop them.

Counterfactual: San Francisco has rent control and subsidies (Title 8). Landlords have the votes to stop construction.

Plus; the probem is *regional8. It's the Bay Area as a whole which is chronically short new housing. SF alone cannot absorb all new demand. Similar dynamics affect most constrained markets.

Again; your economic understanding is flawed, as is your grasp of historical facts.

It is not a counterfactual. Once you have rent control, existing renters will no longer be in favor of building new housing. You're confusing having the votes at two different times, among other things.